## Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph ShalikaHaruzo Hida, Dinakar Ramakrishnan, Freydoon Shahidi In Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger. |

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### Contents

Jeffrey Adams Theta10 | 39 |

Jeffrey D Adler Lawrence Corwin and Paul J Sally Jr Discrete series | 57 |

Don Blasius Elliptic curves Hilbert modular forms and | 83 |

Siegfried Böcherer Masaaki Furusawa and Rainer SchulzePillot On | 105 |

Daniel Bump Solomon Friedberg and Jeffrey Hoffstein Sums of twisted | 131 |

Bill Casselman Harmonic analysis of the Schwartz space | 163 |

RankinSelberg convolutions | 255 |

to theta characteristics | 279 |

Henry H Kim and Freydoon Shahidi On the holomorphy | 561 |

in the Grassmannian | 573 |

Philip Kutzko Types and covers for SL2 | 599 |

Robert P Langlands Beyond endoscopy | 611 |

A question | 699 |

Dinakar Ramakrishnan Existence of Ramanujan primes for GL3 | 711 |

Peter Sarnak Nonvanishing of Lfunctions on Rs1 | 719 |

Joseph A Shalika Ramin TaklooBighash and Yuri Tschinkel Rational | 733 |

four Lfunction of GSp4 | 331 |

symmetric matrices | 421 |

15 | 434 |

Langlands reciprocity law for padic SO2n+1 | 457 |

Katz Larsens alternative moments and the monodromy | 521 |

Joseph A Shalika and Yuri Tschinkel Height zeta functions of equivariant | 743 |

integral structures | 773 |

JeanLoup Waldspurger Représentations de réduction unipotente pour | 803 |